Mister Exam
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How to use it?
- Limit of the function:
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Limit of (8*sin(x)+sin(5*x))/(-sin(4*x)+sin(7*x))
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Limit of (-sin(2*x)+sin(3*x))/(-sin(4*x)+sin(5*x))
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Limit of sin(3)^2/sin(2)^2
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Limit of (-2*sin(x)+sin(2*x))/(5*x^2*log(cos(x)))
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Identical expressions
- sin(three)^ two /sin(two)^ two
- sinus of (3) squared divide by sinus of (2) squared
- sinus of (three) to the power of two divide by sinus of (two) to the power of two
- sin(3)2/sin(2)2
- sin32/sin22
- sin(3)²/sin(2)²
- sin(3) to the power of 2/sin(2) to the power of 2
- sin3^2/sin2^2
- sin(3)^2 divide by sin(2)^2
Limit of the function sin(3)^2/sin(2)^2
The solution
You have entered
[src]
/ 2 \
|sin (3)|
lim |-------|
x->0+| 2 |
\sin (2)/
$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right)$$
Limit(sin(3)^2/sin(2)^2, x, 0)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Rapid solution
[src]
2 sin (3) ------- 2 sin (2)
$$\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
$$\lim_{x \to \infty}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
$$\lim_{x \to \infty}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→oo
$$\lim_{x \to 1^-}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right) = \frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
More at x→-oo
One‐sided limits
[src]
/ 2 \
|sin (3)|
lim |-------|
x->0+| 2 |
\sin (2)/
$$\lim_{x \to 0^+}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right)$$
2 sin (3) ------- 2 sin (2)
$$\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
= 0.0240860321094052
/ 2 \
|sin (3)|
lim |-------|
x->0-| 2 |
\sin (2)/
$$\lim_{x \to 0^-}\left(\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}\right)$$
2 sin (3) ------- 2 sin (2)
$$\frac{\sin^{2}{\left(3 \right)}}{\sin^{2}{\left(2 \right)}}$$
= 0.0240860321094052
= 0.0240860321094052
The graph